The present invention relates generally to modeling of the propagation of a pharmaceutical in a patient, and, particularly, to modeling of contrast media propagation in a patient for use in imaging procedures.
References set forth herein may facilitate understanding of the present invention or the background of the present invention. Inclusion of a reference herein, however, is not intended to and does not constitute an admission that the reference is available as prior art with respect to the present invention.
Various contrast media are injected into a patient for many diagnostic and therapeutic imaging procedures such as X-ray procedures (including, for example, angiography, venography and urography), computed tomography (CT), magnetic resonance imaging (MRI), ultrasonic imaging, light based imaging, and positron emission tomography (PET). The CT scanner has, for example, become an indispensable modern, diagnostic imaging tool. It enables the precise measurement of anatomical structures, and in some instances, physiologic processes in 2, 3 and 4 dimensions. The imaging of soft tissue, vasculature, and other structures is not easily accomplished with CT scanners because these structures do not differentially attenuate X-Rays to an appreciable degree. To overcome these limitations, a radio-absorbing or radio-opaque drug or contrast is injected, commonly into the peripheral venous circulation. The contrast agent used for CT imaging is typically a water-soluble salt that binds three or more Iodine atoms within a benzene structure. Iodine attenuates X-Rays in the energy ranges used in medical imaging procedures. A computer-controlled pump or injector injects a precise volume of contrast agent at flow rates typically ranging from 0.5 to 6 ml/s (pressures generated up to 300 psi) into a patient's venous system before a scan is made. Examples of front loading syringe injectors commonly used in CT procedures are disclosed, for example, in U.S. Pat. Nos. 5,300,031, 5,383,858 and 6,652,489, the disclosure of which is incorporated herein by reference.
The MultiDetector CT scanners (MDCT) now enable clinicians to perform unparalleled diagnostic scans of patient anatomy and physiology. With such new technologies, however, arise new challenges for application in daily practice. Despite the breakthroughs in volumetric coverage and image resolution, the new generation of CT scanners still requires the administration of iodinated contrast agent to achieve the best image and diagnosis. Moreover, the importance of timing of the scan to coincide with optimal contrast concentration can be increased in the case of MDCT.
The delivery of contrast agent is generally open-loop in the sense that the injection system does not incorporate knowledge or estimates of the drug's interaction with the physiology into its control scheme. The injection system delivers exactly the amount of contrast agent programmed at the specified rate. This methodology works well when a scan takes a substantial amount of time so that the early pharmacokinetics of the drug does not influence the quality of the diagnostic scan. This methodology also works well when the object of the scan is an assessment of perfusion, that is drug uptake, into, for example, parenchyma or suspected carcinomas. Advances in scanning technology enable the acquisition of images in very short time periods (seconds). This trend, coupled with the increasing desire to produce volumetric renderings of anatomical structures (like the heart, its coronary vasculature, and the great vessels leading to and from it), requires that the early pharmacokinetics and pharmacodynamics of the contrast be considered. Ideally, the attenuation curve produced by the presence of contrast agent in a large blood vessel is preferably uniform (flat) and sufficiently similar across regions of the patient to facilitate volumetric rendering and accurate diagnosis, and the imaging scan is timed to coincide with optimal contrast concentration in the region(s) of interest.
Differences in dosing requirements for different patients during imaging and other procedures have been recognized. For example, U.S. Pat. No. 5,840,026, assigned to the assignee of the present invention, the disclosure of which is incorporated herein by reference, discloses devices and methods to customize the injection to the patient using patient specific data derived before or during an injection. Although differences in dosing requirements for medical imaging procedures based upon patient differences have been recognized, conventional medical imaging procedures continue to use pre-set doses or standard delivery protocols for injecting contrast media during medical imaging procedures. Given the increased scan speed of recently available CT scanners including MDCT scanners, single phase injections are dominant over biphasic injections in regions of the world where such fast scanners are used. Although using fixed protocols (whether uniphasic, biphasic or multiphasic) for delivery simplifies the procedure, providing the same amount of contrast media to different patients under the same protocol can produce very different results in image contrast and quality. Furthermore, with the introduction of the newest MDCT scanners, an open question in clinical practice and in the CT literature is whether the standard contrast protocols used with single-slice, helical scanners will translate well to procedures using the MDCT machines. Cademartiri, F. and Luccichenti, G., et al. (2004). “Sixteen-row multislice computed tomography: basic concepts, protocols, and enhanced clinical applications.” Semin Ultrasound CT MR 25(1): 2-16.
A few studies have attempted quantitative analyses of the injection process during CT angiography (CTA) to improve and predict arterial enhancement. For example, Bae and coworkers developed pharmacokinetic (PK) and dynamic models of the contrast behavior and solved the coupled differential equation system with the aim of finding a driving function that causes the most uniform arterial enhancement. K. T. Bae, J. P. Heiken, and J. A. Brink, “Aortic and hepatic contrast medium enhancement at CT. Part I. Prediction with a computer model,” Radiology, vol. 207, pp. 647-55, 1998; K. T. Bae, “Peak contrast enhancement in CT and MR angiography: when does it occur and why? Pharmacokinetic study in a porcine model,” Radiology, vol. 227, pp. 809-16, 2003, K. T. Bae et al., “Multiphasic Injection Method for Uniform Prolonged Vascular Enhancement at CT Angiography: Pharmacokinetic Analysis and Experimental Porcine Method,” Radiology, vol. 216, pp. 872-880, 2000, U.S. Pat. Nos. 5,583,902, 5,687,208, 6,055,985, 6,470,889 and 6,635,030, the disclosures of which are incorporated herein by reference. An inverse solution to a set of differential equations of a simplified compartmental model set forth by Bae et al. indicates that an exponentially decreasing flow rate of contrast medium may result in optimal/constant enhancement in a CT imaging procedure.
Bae's PK approach for deriving uniform image enhancement relies upon many physiological parameters that may not be readily available to a clinician, such as central blood volume, diffusion rates, and cardiac output. Not having explicit measurements of cardiac output is a substantial drawback to Bae's approach, despite attempts to approximate the value based upon the patient's age, weight, and height. Furthermore, there is no consideration for implementation of the PK models in a controller framework. The injection profiles computed by inverse solution of the PK model are profiles not readily realizable by CT power injectors, without major modification. Moreover, the PK model of Bae does not consider the effects of pulsatile flow, vessel compliance, and local blood/contrast parameters (i.e., viscosity).
Fleischmann and coworkers treat the cardiovascular physiology and contrast kinetics as a “black box” and determine its impulse response by forcing the system with a short bolus of contrast (approximating an unit impulse). In that method, one performs a Fourier transform on the impulse response and manipulates this transfer function estimate to find the optimal injection trajectory. D. Fleischmann and K. Hittmair, “Mathematical analysis of arterial enhancement and optimization of bolus geometry for CT angiography using the discrete Fourier transform,” J Comput Assist Tomogr, vol. 23, pp. 474-84, 1999, the disclosure of which is incorporated herein by reference.
The administration of contrast agent is commonly uniphasic—100 to 150 mL of contrast at one flow rate, which results in a non-uniform enhancement curve. See, for example, D. Fleischmann and K. Hittmair, supra; and K. T. Bae, “Peak contrast enhancement in CT and MR angiography: when does it occur and why? Pharmacokinetic study in a porcine model,” Radiology, vol. 227, pp. 809-16, 2003, the disclosure of which are incorporated herein by reference. Fleischmann and Hittmair present a scheme that attempts to tailor the administration of contrast agent into a biphasic injection tailored to the individual patient with the intent of optimizing imaging of the aorta. A fundamental difficulty with controlling the presentation of CT contrast agent is that hyperosmolar drug diffuses quickly from the central blood compartment. Additionally, the contrast is mixed with and diluted by blood that does not contain contrast. The mixing and dilution of the contrast medium is reflected by a peaked and distorted enhancement curve as exemplified in FIG. 1.
Fleischmann proscribes that a small bolus injection, a test injection, of contrast agent (16 ml of contrast at 4 ml/s) be injected prior to the diagnostic scan. A dynamic enhancement scan is made across a vessel of interest. The resulting processed scan data (test scan) is interpreted as the impulse response of the patient/contrast medium system. Fleischmann derives the Fourier transform of the patient transfer function by dividing the Fourier transform of the test scan by the Fourier transform of the test injection. Assuming the system is a linear time invariant (LTI) system and that the desired output time domain signal is known (a flat diagnostic scan at a predefined enhancement level) Fleischmann derives an input time signal by dividing the frequency domain representations of the desired output by that of the patient transfer function.
The approach of Fleischman may be promising in the fact that it derives a representation of the patient based upon a known test injection. Because the method of Fleischmann et al. computes input signals that are not realizable in reality as a result of injection system limitations (for example, flow rate limitations), one must truncate and approximate the computed continuous time signal. Because of the inaccuracies introduced by that step, the computed idealized input trajectories are not optimal. Furthermore, it is unclear if the linearity assumption holds for all patients and pathophysiologies. Finally, it is unclear if the enhancement curves generated by his method are any more uniform than those generated by simple biphasic injections.
Various models have also been developed for pharmaceuticals other than contrast media. For example, Fisher and Teo, “Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics”, IEEE Trans Biomed Eng, vol. 36(4), pp. 479-486, 1989, the disclosure of which is incorporated herein by reference, modeled the dynamics of glucose and insulin with the aim of generating optimal insulin infusion parameters. They treat the problem as a classic optimization problem by applying a quadratic performance criterion and solving the algebraic Ricatti equations. They discovered that impulse control was the superior approach compared to constant infusion, sub-optimal control and no regulation of the insulin injection.
Jacobs “Algorithm for optimal linear model-based control with application to pharmacokinetic model-driven drug delivery”, IEEE Trans Biomed Eng, vol. 37(1), pp. 107-109, 1990, the disclosure of which is incorporated herein by reference, presented a control algorithm for the regulation of anesthetic drugs that places a pharmacokinetic model in parallel with the actual drug process. A clinician determines the target plasma concentration.
Wada and Ward, “The hybrid model: a new pharmacokinetic model for computer-controlled infusion pumps”, IEEE Trans. Biomed Eng, vol. 41(2), pp. 134-142, 1994, the disclosure of which is incorporated herein by reference, derived a 3 compartment pharmacokinetic model similar to the approach taken by Bee and used this in a hybrid control scheme in an attempt to regulate the plasma concentration of anesthetic (the upload alienating). They were attempting to model the recirculation effect of the agent through the blood stream, as well, which they modeled by inserting transport delays in their simulations. They were able to generate simulation with prediction errors under 5%.
Wada and Ward “Open loop control of multiple drug effects in anesthesia”, IEEE Trans. Biomed Eng, vol. 42(7), pp. 666-677, 1995, the disclosure of which is incorporated herein by reference, also applied their hybrid pharmacokinetic (PK) model to control multiple effects of anesthetic drugs. Their control scheme requires an anesthesiologist to set the allowable side-effect levels (expressed as a plasma concentration).
Neatpisarnvanit and Boston, “Estimation of plasma insulin from plasma glucose”, IEEE Trans Biomed Eng, vol. 49(11), pp. 1253-1259, 2002, the disclosure of which is incorporated herein by reference, applied a recursive least square parameter estimation approach to predict the plasma concentration of glucose and insulin. Their approach resulted in predictions that matched plasma levels of glucose and insulin in 6 of 7 patients (experimental data gathered via the IntraVenous Glucose Tolerance Test) and agreed favorably. Gentilini et al. “A new paradigm for the closed-loop intraoperative administration of analgesics in humans”, IEEE Tran Biomed Eng, vol. 49(4), pp. 289-299, 2002, the disclosure of which is incorporated herein by reference, proposed a model predictive control (MPC) approach for controlling the plasma concentration of the opiate alfentanil with a computer controlled infusion pump. The pharmacokinetic model was a 3-compartment model describing the distribution of the opiate in a human. The controller relied upon an observer that estimates plasma concentrations of the drug based on measurements of mean arterial pressure and a PK model running in parallel. Gentilini et al. placed constraints on the maximum concentration to prevent overdosing. They also filtered disturbances in the mean arterial pressure measurements and allowed for the controller to act faster or slower depending on the state of the patient (that is, hypo vs. hypertensive).